Question: The probability of selecting an even integer at random from a list of $30$ integers is $\frac{7}{10}$. How many odd integers are in the list?
Explanation: Since every number is either even or odd but not both, the probabilities of selecting even and odd integers must add to $1$. The probability of selecting an odd integer is thus $1-\frac{7}{10}=\frac{3}{10}$, so $\frac{3}{10}$ of the $30$ integers are odd. Therefore, there are $\frac{3}{10}(30)=\boxed{9}\text{ integers}$ that are odd in the list.